589 
ON THE 
MOTION OF A PROJECTILE IN A RESISTING MEDIUM, 
{Continued from p. 139.) 
BY 
A. G. GREENHILL, M.A., 
(Professor of Mathematics to the Advanced Class of Artillery Officers .) 
When the resistance varies as the cube of the velocity, the trajectory 
was shown in the Proceedings/ ; of the R. A. Institution, Yol. XI., 
p. 138, to be expressed by,— 
and 
where 
1 + a* 1 
J> a VV(H« ! )I + ^ 
w 2 r x d x 
y- ax ~i-jgkf y+a’ 
_ (4 + (4 + 4 a 2 )* gx 
x ' vs w ’ 
Y __ sn x dn x _ sn a dn a 
(1—cnx) 2 ’ ~”(l--cna) 2 ’ 
^ 1 1-— cn a 
2^/2 k 1 + k cn a 5 
a — 
7(t5-W 
(cn a—cn 2X) (cna—cn 2<oX) (cn a—cn 2o> 2 Jf) 
(cn fX—cna) (cn fwX— cn a) (cn cn a) 
the tangent of the inclination to the horizon at the origin, where 
the velocity is infinite, the modulus k being sin 15°; 
and w is the terminal velocity in the medium; so that the retardation 
of the projectile, due to the resistance when the velocity is v, is g (— ) . 
Therefore, putting 
lc +lcna _ 1 
1— cn a 26^/2’ 
73 
